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New Demiclosedness Principles for (Firmly) Nonexpansive Operators

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Computational and Analytical Mathematics

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 50))

Abstract

The demiclosedness principle is one of the key tools in nonlinear analysis and fixed point theory. In this note, this principle is extended and made more flexible by two mutually orthogonal affine subspaces. Versions for finitely many (firmly) nonexpansive operators are presented. As an application, a simple proof of the weak convergence of the Douglas-Rachford splitting algorithm is provided.

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Acknowledgements

HHB thanks Patrick Combettes and Jonathan Eckstein for their pertinent comments. HHB was partially supported by the Natural Sciences and Engineering Research Council of Canada and by the Canada Research Chair Program.

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Authors and Affiliations

  1. Department of Mathematics, University of British Columbia, Kelowna, BC, V1V 1V7, Canada

    Heinz H. Bauschke

Authors
  1. Heinz H. Bauschke
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Correspondence to Heinz H. Bauschke .

Editor information

Editors and Affiliations

  1. Lawrence Berkeley National Laboratory, Berkeley, USA

    David H. Bailey

  2. Mathematics, University of British Columbia, Kelowna, British Columbia, Canada

    Heinz H. Bauschke

  3. Dept. Mathematics & Statistics, Simon Fraser University, Burnaby, British Columbia, Canada

    Peter Borwein

  4. Mathematics, University of Florida, Gainesville, Florida, USA

    Frank Garvan

  5. Mathematics and Computer Science, University of Limoges, Limoges, France

    Michel Théra

  6. Mathematics and Computer Science Department, La Sierra University, Riverside, California, USA

    Jon D. Vanderwerff

  7. Dept. Combinatorics & Optimization, University of Waterloo Faculty of Mathematics, Waterloo, Ontario, Canada

    Henry Wolkowicz

Additional information

Dedicated to Jonathan Borwein on the occasion of his 60th birthday

Communicated By Michel Théra.

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Bauschke, H.H. (2013). New Demiclosedness Principles for (Firmly) Nonexpansive Operators. In: Bailey, D., et al. Computational and Analytical Mathematics. Springer Proceedings in Mathematics & Statistics, vol 50. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7621-4_2

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